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Inspired by this view, based on the hippocampal CA3\u2013CA1 synaptic network model of memory we constructed earlier, we encode memory engrams as trajectories within the SHC in phase space. Short-term memory is transformed into long-term memory and then is encoded as trajectories within the SHC. The saddle points indicate the information blocks that have been segmented during the process of short-term memory. A stable heteroclinic network (SHN) is composed of multiple SHCs, whose trajectories express the memory engrams formed after the conversion of multiple short-term memories into long-term memories. From the existence conditions of SHC and SHN, the asymmetric regulation of neurotransmitters such as acetylcholine on the inhibition strength of adjacent postsynaptic neurons determines the capacity of short-term memory and participates in the encoding of long-term memory. Numerical results reveal the hysteresis effect of saddle points on the trajectories that reflect the limited capacity of short-term memory. All saddle points in the SHNs enable long-term memory to possess an extremely large capacity. Moreover, while noise in the hippocampal circuit can lead to the loss or confusion of memory information, it can also facilitate the encoding of long-term memories. The model and its theoretical analysis allow us to explain memory from the perspective of dynamics and have guiding significance for understanding the encoding and storage process of memory.<\/jats:p>","DOI":"10.1063\/5.0223045","type":"journal-article","created":{"date-parts":[[2024,12,3]],"date-time":"2024-12-03T16:00:42Z","timestamp":1733241642000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":3,"title":["Hippocampus encoding memory engrams as stable heteroclinic network"],"prefix":"10.1063","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-0196-0945","authenticated-orcid":false,"given":"Lei","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Northwestern Polytechnical University 1 , Xi\u2019an 710129,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8765-0457","authenticated-orcid":false,"given":"Honghui","family":"Zhang","sequence":"additional","affiliation":[{"name":"MIIT Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University 2 , Xi\u2019an 710129,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0115-7750","authenticated-orcid":false,"given":"Zhongkui","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Northwestern Polytechnical University 1 , Xi\u2019an 710129,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2024,12,3]]},"reference":[{"issue":"6473","key":"2024120315113854400_c1","doi-asserted-by":"publisher","first-page":"eaaw4325","DOI":"10.1126\/science.aaw4325","article-title":"Memory engrams: Recalling the past and imagining the future","volume":"367","year":"2020","journal-title":"Science"},{"key":"2024120315113854400_c2","volume-title":"Cognitive Neuroscience: The Biology of the Mind","year":"2011","edition":"3"},{"issue":"24","key":"2024120315113854400_c3","doi-asserted-by":"publisher","first-page":"10464","DOI":"10.1523\/JNEUROSCI.18-24-10464.1998","article-title":"Synaptic modifications in cultured hippocampal neurons: Dependence on spike timing, synaptic strength, and postsynaptic cell type","volume":"18","year":"1998","journal-title":"J. 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